Question

Which of the following graphs to the probability that z-score is between 0 and 1?

Answer 1

The z-score of a measure is given by the following formula

$z=\frac{x-\mu}{\sigma}$

where x represents the measure, mu represents the mean of the distribution, and sigma represents the standard deviation.

If we have a z-score equal to zero, our measure will be

$\begin{gathered} 0=\frac{x-\mu}{\sigma} \\ 0=x-\mu \\ x=\mu \end{gathered}$

a z-score equal to zero represents the mean of the distribution.

For a z-score equal to 1, we have

$\begin{gathered} 1=\frac{x-\mu}{\sigma} \\ \sigma=x-\mu \\ x=\mu+\sigma \end{gathered}$

Then, the interval between z = 0 and z = 1 is the interval between the mean and one positive standard deviation.

$(\mu,\mu+\sigma)$

The graph that represents this interval is the first graph.